Find the perimeter of rectangle ABCD if the bisector of angle B intersects side AD at point

| September 6, 2021 | education

Find the perimeter of rectangle ABCD if the bisector of angle B intersects side AD at point E and divides it into segments AE = 17cm and ED = 21cm.

The perimeter of a given rectangle can be found using the following formula:

P = 2 * (AB + AD).

We can find the AD side right away, because it is equal to

AD = AE + ED.

Let’s find its length:

AD = 17 + 21 = 38 cm.

The bisector BE bisects the angle B. This means that the angle ABE is 45º. Consider a triangle ABE. It is rectangular with right angle A, angle B is 45º. Find the angle E:

Angle E = 180º – 90º – 45º = 45º.

Hence, angle B = angle E = 45º. It turns out that triangle ABE is isosceles and in it the sides AB and AE are equal. From here

AB = AE = 17 cm.

Now, knowing both sides of the rectangle, we can find its perimeter. Let’s find it:

P = 2 * (17 + 38) = 110 cm.

Answer: The perimeter of rectangle ABCD is 110 cm.



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